Be able to identify which triangles can be constructed by the methods:

1. Constructing & Proving Congruent Triangles Study Guide Name:____________________ Your exam will be on _________________ You may use the study guide on the exam only if you have completed every problem. Be able to identify which triangles can be constructed by the methods: SSS, SAS, AAS, ASA, SsA, or HL. Be able to construct those triangles that can be constructed and identify the method. 1. Construct ABC with 2. Construct DEF with AB = 3”, BC = 2” , CA = 3” DE = 3”, mE=86, EF = 2” 3. Construct GHI with 4. Construct JKL with mG=35, GH = 3”, HI = 2” mL=59, KL = 2”, JK = 3” Hint: SSS Hint: SAS Hint: ASS Hint: SsA p.1

2. 5. Construct MNO with 6. Construct PRQ with mM=35, MN = 3”, mN=86, PR = 3”, mR=86,mQ=59 7. Construct STU with 8. Construct VYX with mS=35, mT=86, mU=59 mV=90, XV = 4”, YX = 5” Hint: ASA Hint: AAS Hint: AAA Hint: SsA or HL p.2

3. You may use the study guide on the exam only if you have completed every problem. Name the two pair of alternate interior angles: ___________ & ___________ and ___________ & ___________ Name the vertical angles in the triangles: ___________& ___________ Name the side included by VPR and V :__________ Name the pair of congruent angles created if GH bisectors QGR: _______________ & _________________ Name the pair of congruent angles created if GH bisectors QHR: _______________ & _________________ Name the angle included by QH and QG: __________ Name the pair of congruent segments created if W is the midpoint of OT: _______________ & _________________ Name the vertical angles in the triangles: ___________& ___________ Name the angle opposite BO: __________ Name the side opposite I:___________ p.3

4. Name the right angles formed BE  AD: _______________ & _________________ Name the right angles formed AE  CD: _______________ & _________________ Name the part in the overlapping triangles that is congruent to itself by Reflexive Property. _______________ E C A B D Name the pair of congruent segments created if N is the midpoint of JK: _______________ & _________________ Name the part in both triangles that is congruent to itself by Reflexive Property. _______________ Name the hypotenuse: ______________________________ Name the legs: ____________________________________ Which pair of triangles can be assumed congruent by SsA? ________ A. B. Write the congruence statement for those triangles. ______________________________________ p.4

5. You may use the study guide on the exam only if you have completed every problem. Copy the SSS congruence theorem: Find and copy or complete this proof: Copy the SAS congruence theorem Find and copy or complete this proof: X Given: XA = YA and XC =YC Prove: XACYAC A C Y Hint: to prove ∆XAC∆YAC apply reflexive property & SSS To XACYAC apply CPCF Hint: to prove ∆JUE∆ILU apply vertical angles & SAS To JELIapply CPCF p.5

6. You may use the study guide on the exam only if you have completed every problem. Copy the ASA congruence theorem: Find and copy or complete this proof: Copy the AAS congruence theorem: Find and copy or complete this proof: A Given: mADB = mCDB mABD = mCBD Prove: AB= CB D C B Hint: to prove ∆ABD∆CBD apply reflexive property & ASA To AB=CBapply CPCF Hint: to prove ∆PRS∆TQR apply reflexive property & AAS p.6

7. You may use the study guide on the exam only if you have completed every problem. Copy the SsA congruence theorem: Find and copy or complete this proof: Copy the HL congruence theorem: Find and copy or complete this proof: Given: ON > OG, ON  FE OG  GE To prove: GNO   GFE Hint: to prove ∆GNO∆GFE vertical angles & SsA V Given: VXWY and WZ = VY XZ = XY Prove: W  V Z W Y X Hint: to prove ∆WXZ∆VXY apply HL or SsA To WVapply CPCF p.7